Classification of periodic linear groups over fields of odd characteristic
type: Item
instance of: scholarly article
title: Classification of periodic linear groups over fields of odd characteristic
zbMATH Open document ID: 0545.20034
DOI: 10.1007/BF00971460
published in: Siberian Mathematical Journal
publication date: 1984-01-01T00:00:00Z
review text: The problem of classifying simple periodic linear groups was formulated by V. P. Platonov. The author gives a solution of this problem for fields of characteristic \(p>2\), proving the following theorem: Each completely reducible infinite simple periodic linear group over a field of characteristic \(p>2\) contains a subgroup of finite index, which is isomorphic to the central product of an Abelian p'-group and a finite set of Chevalley groups or their twisted analogs over an algebraic extension of a simple finite field. The main idea of the proof of this theorem is based on the method developed by V. P. Shunkov which consists in the investigation of the centralizers of involutions of the groups considered.
Mathematics Subject Classification ID: 20G40
Mathematics Subject Classification ID: 20E07
Mathematics Subject Classification ID: 20E32
zbMATH DE Number: 3867581
zbMATH Keywords: simple periodic linear groups
zbMATH Keywords: completely reducible infinite simple periodic linear group
zbMATH Keywords: subgroup of finite index
zbMATH Keywords: central product
zbMATH Keywords: Chevalley groups
zbMATH Keywords: centralizers of involutions
author: Alexandre V. Borovik
reviewed by: Nikolai I. Osetinski
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf00971460
OpenAlex ID: W2074733294
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description: scientific article; zbMATH DE number 3867581